Question

На стороне ВС прямоугольника АВСД , у которого АВ =30 отмечена точка Е так,что ДЕ=34 И угол ВЕА=45градусов . Найдите АД. Подробно,пожалуйста

Answer 1

Ав=сд=30
треугольник есд- прямоугольный
ес^2=ед^2-дс^2(из теаремы пифагора)
ес^2=1156-900
ес^2=256
ес=16
треугольник авс= треугольник есд( по катету и острому углу)
ве=16
ад=ве+ес
ад=32

Answer 2

Finding AD in Rectangle ABCD

To find the length of AD in rectangle ABCD, we can use the given information that AB = 30, DE = 34, and angle BEA = 45 degrees.

Let's break down the problem step by step:

1. Draw rectangle ABCD with points A, B, C, and D. 2. Mark point E on side AB such that DE = 34. 3. Draw a line from E to point A, forming triangle ADE. 4. Since angle BEA = 45 degrees, angle DEA is also 45 degrees (as opposite angles in a rectangle are equal). 5. Now, we have a right triangle ADE with angle DEA = 45 degrees and DE = 34. 6. To find AD, we can use trigonometric ratios. 7. In a right triangle, the tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. 8. In triangle ADE, the tangent of angle DEA is equal to the ratio of DE to AD. 9. Therefore, we can write the equation: tan(45 degrees) = DE / AD.

Now, let's solve the equation to find AD.

Using a calculator or trigonometric table, we know that the tangent of 45 degrees is 1.

Therefore, we can rewrite the equation as: 1 = 34 / AD.

To find AD, we can cross-multiply and solve for AD:

AD = 34 / 1

AD = 34

Therefore, the length of AD in rectangle ABCD is 34.

Please note that the solution assumes that the given information and diagram are accurate.